Existence of bounded solutions for nonlinear hyperbolic partial differential equations

Abstract

In this article we first establish a new representation formula for bounded solutions to a class of nonlinear second-order hyperbolic partial differential equations. Next, we use of our newly-established representation formula to establish the existence of bounded solutions to these nonlinear partial differential equations.

Keywords

• Hyperbolic partial differential equations
• bounded solutions
• almost automorphic
• pseudo-almost automorphic